Apple TV (2nd gen) setup w/o remote

Welcome to the Apple Community.

My best advice, in my opinion, is to recommend you purchase a replacement remote, however, if you are averse to this suggestion there are some workarounds which may apply in some situations.

Depending on which Apple TV you have you may be able to set up the Apple TV from your mobile device. You will need a 3rd generation Apple TV for later running software version 6.0 or later and an iOS device running iOS 9.1 or later.

Restore your Apple TV. When the Apple TV setup screen appears, unlock your iOS device and make sure Bluetooth and Wi-Fi are turned on. Touch your iOS device to Apple TV and follow the onscreen instructions on your iOS device and Apple TV.

Automatic setup doesn’t transfer account information for third-party apps such as Netflix or Hulu and doesn’t turn on iTunes Match or Home Sharing.

If this doesn't work, you don't have an iOS mobile device or your equipment doesn't meet the minimum requirements, you may wish to look at ciderTV for Mac OSX, once you have installed the app on your Mac...

1. Check that Bluetooth is On & Discoverable;
2. Keep Bluetooth preferences window open during pairing;
3. Connect Apple TV to your Mac via USB cable and reset it in iTunes app;
4. Turn Apple TV on and wait until it finds your Mac. A pop-up window will appear that says “Pairing Request from Apple TV”;
5. Tap "Pair";
6. You will see CiderTV control interface with buttons.

You can purchase a replacement remote from Apple

Be aware that the 2nd gen is considered obsolete so there may be things that it won't support and if certain issues arise there may not be a lot that can be done.

If you are able to borrow a remote (both the white ones and the silver ones will work), you can of course install the remote app on a mobile device and use that.